A024347 Expansion of 1/((1-x)*(1-6*x)*(1-9*x)*(1-12*x)).

1, 28, 523, 8218, 117649, 1592416, 20790631, 264958246, 3320750557, 41132364364, 505211150899, 6167574174034, 74958865496425, 908053837462072, 10973667150086527, 132377759927894782, 1594780291608334453

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (28,-261,882,-648).

Crossrefs

Cf. A003464, A016244, A024346.

Programs

Magma

m:=25; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-6*x)*(1-9*x)*(1-12*x)))); // Vincenzo Librandi, Jul 16 2013

Magma

I:=[1, 28, 523, 8218]; [n le 4 select I[n] else 28*Self(n-1)-261*Self(n-2)+882*Self(n-3)-648*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 16 2013

Maple

A024347:= n -> (20*12^(n+3) - 55*9^(n+3) + 44*6^(n+3) -9)/3960; seq(A024347(n), n=0..20); # G. C. Greubel, Jan 30 2022

Mathematica

CoefficientList[Series[1/((1-x)(1-6x)(1-9x)(1-12x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 16 2013 *)

PARI

Vec(1/((1-x)*(1-6*x)*(1-9*x)*(1-12*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Sage

[(20*12^(n+3) - 55*9^(n+3) + 44*6^(n+3) -9)/3960 for n in (0..20)] # G. C. Greubel, Jan 30 2022

Formula

a(n) = (20*12^(n+3) - 55*9^(n+3) + 44*6^(n+3) - 9)/3960. - Yahia Kahloune, Jun 28 2013

a(n) = 28*a(n-1) - 261*a(n-2) + 882*a(n-3) - 648*a(n-4) for n > 3; a(0)=1, a(1)=28, a(2)=523, a(3)=8218. - Vincenzo Librandi, Jul 16 2013

E.g.f.: (-9*exp(x) + 9504*exp(6*x) - 40095*exp(9*x) + 34560*exp(12*x))/3960. - G. C. Greubel, Jan 30 2022